Bao, Zhiqiang Intersection theory in homogeneous spaces of simple Lie groups. (Chinese. English summary) Zbl 1025.22009 Acta Sci. Nat. Univ. Pekin. 35, No. 3, 297-301 (1999). Summary: Consider \(H^*(U_n/T_n,\mathbb{Z})\), the integral cohomology ring of the homogeneous space \(U_n/T_n\). It is a quotient ring of the polynomial ring in \(n\) variables. Particularly, the homogeneous part with degree \(d=\dim U_n/T_n\) corresponds to the highest dimensional cohomology group \(\mathbb{Z}\), i.e., each degree \(d\) homogeneous polynomial \(f\) corresponds to an integer \(\chi(f)\). The present article computes this correspondence explicitly. The connections with the intersection theory of the manifold \(U_n/T_n\) are also discussed. A similar result applies to the homogeneous space \(Sp_n/T_n\). MSC: 22E46 Semisimple Lie groups and their representations 57T15 Homology and cohomology of homogeneous spaces of Lie groups Keywords:simple Lie group; homogeneous space; intersection theory PDFBibTeX XMLCite \textit{Z. Bao}, Acta Sci. Nat. Univ. Pekin. 35, No. 3, 297--301 (1999; Zbl 1025.22009)